Electron nuclear double resonance (ENDOR)

1. Electron nuclear double resonance (ENDOR) Gavin W Morley, Department of Physics, University of Warwick

2. Electron nuclear double resonance (ENDOR) Overview Why do ENDOR? Continuous-wave ENDOR Pulsed ENDOR with: Selective pulses Non-selective pulses

3. Electron nuclear double resonance (ENDOR) Why do ENDOR? More sensitive than NMR “EPR-detected NMR” (electron has a larger magnetic moment, flips faster and can be detected more sensitively) NMR may be impossible due to nearby electron spin Higher resolution than EPR Extra selection rules

4. Birth of ENDOR George Feher (born 1924) Photo from AIP Emilio Segre Visual Archives Image by Manuel Vögtli (UCL)

5. Electron nuclear double resonance (ENDOR) EPR-detected NMR: how?

6. Electron paramagnetic resonance Iz = ½ Iz = -½ Photons reflected S = ½ I = ½ Magnetic field, B Energy of a spin system Magnetic field, B

7. Electron paramagnetic resonance Iz = ½ Iz = -½ Photons reflected S = ½ I = ½ Magnetic field, B Energy of a spin system You need to record an EPR spectrum before trying ENDOR Magnetic field, B

8. ENDOR Iz = ½ Iz = -½ Photons reflected S = ½ I = ½ Magnetic field, B Energy of a spin system RF in Magnetic field, B

9. Two ENDOR transition frequencies For isotropic A Microwave photons reflected “Weak coupling” RF frequency Microwave photons reflected “Strong coupling” RF frequency

10. Electron paramagnetic resonance Iz = ½ Iz = -½ Photons reflected Magnetic field, B Energy of a spin system Magnetic field, B

11. Electron paramagnetic resonance Energy of a spin system Magnetic field, B

12. Electron nuclear double resonance (ENDOR) • EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

13. Electron nuclear double resonance (ENDOR) • EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

14. Electron nuclear double resonance (ENDOR) • EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

15. Electron nuclear double resonance (ENDOR) • EPR-detected NMR: how? B0 is static magnetic field B1 is EPR magnetic field B2 is NMR magnetic field

16. Continuous Wave ENDOR EPR-detected NMR George Feher Photo from AIP Emilio Segre Visual Archives Image by Manuel Vögtli (UCL)

17. Continuous Wave ENDOR

18. Continuous Wave ENDOR

19. Continuous Wave ENDOR CW ENDOR is the desaturation of a saturated EPR transition by providing an extra T1e relaxation route via NMR

20. Continuous Wave ENDOR Hale & Mieher, Phys Rev 184 739 (1969) (following Feher, Phys Rev 114, 1219 (1959)) (use FM and lock-in) νNMR(MHz) CW ENDOR is the desaturation of a saturated EPR transition by providing an extra T1e relaxation route via NMR

21. Continuous Wave ENDOR Hale & Mieher, Phys Rev 184 739 (1969) (following Feher, Phys Rev 114, 1219 (1959)) νNMR(MHz) B Koiller, R B Capaz, X Hu and S Das Sarma, PRB 70, 115207 (2004) Image by Manuel Vögtli (UCL)

22. Continuous Wave ENDOR Hale & Mieher, Phys Rev 184 739 (1969) (following Feher, Phys Rev 114, 1219 (1959)) νNMR(MHz) CW ENDOR effect is typically a few % of the EPR signal

23. Continuous Wave ENDOR Advantage of CW ENDOR: Observe sharpest ENDOR resonances Disadvantage of CW ENDOR: CW ENDOR line intensity depends on a delicate balance between relaxation rate and excitation power. Jack Freed did the relaxation theory for this for molecules in solution. George Feher Photo from UCSD This is compared with experiments in solution in: Plato, Lubitz & Mobius, J Phys Chem 85, 1202 (1981)

24. Pulsed ENDOR • Use a π pulse for nuclei, but there are two main pulse sequences for electrons: • Davies ENDOR: π pulse then echo readout with all selective (long) pulses. • Mims ENDOR uses a stimulated echo with non-selective (short) pulses

25. Davies ENDOR π/2 π π MW: π Roy Davies, Royal Holloway, University of London RF: As with CW ENDOR, sweep RF frequency to get a spectrum. Use long, selective MW pulses to burn a hole  smaller signal. However, there are no “blind spots” which is an advantage over Mims ENDOR.

26. Rotating frame

27. Rotating frame

28. Spin echo In rotating frame

29. Spin echo In rotating frame

30. Davies ENDOR Product operator notation: Electron-nuclear two-spin order, 2SzIz

31. Davies ENDOR RF pulse duration is an important parameter to set

32. Davies ENDOR Davies ENDOR efficiency, FDavies= 50% Echo height RF frequency

33. Davies ENDOR Product operator notation: Electron-nuclear two-spin order, 2SzIz Start again…

34. Davies ENDOR Off-resonance RF does nothing

35. Davies ENDOR Echo height RF frequency

36. Davies ENDOR Product operator notation: Electron-nuclear two-spin order, 2SzIz Start again again…

37. Davies ENDOR

38. Davies ENDOR Davies ENDOR efficiency, FDavies= 50% Echo height RF frequency

39. Davies ENDOR Davies ENDOR disadvantage: selective pulses on electron spins mean many spins are ignored if the resonance is inhomogeneously broadened

40. Mims ENDOR MW: τ τ π RF: sweep RF frequency Non-selective (short) MW pulses excite more spins  bigger signal. However, ENDOR efficiency, FMims = ¼ (1 – cos (Aτ)) so there are “blind spots” with no signal for some τ

41. Mims ENDOR

42. Beware Mims ENDOR blind spots C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991) ENDOR efficiency, FMims = ¼ (1 – cos (Aτ))

43. Beware short RF pulses in pulsed ENDOR C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991) This problem is avoided by “time-domain pulsed ENDOR”, instead of the standard frequency domain experiments.

44. Pulsed ENDOR For more details including TRIPLE (ENDOR with two RF frequencies) see: Schweiger & Jeschke, Principles of pulse electron paramagnetic resonance, OUP 2001 C Gemperle & A Schweiger, Chem Rev 91, 1481 (1991)

45. ENDOR conclusions ENDOR is much more sensitive than NMR and has much higher resolution than EPR Continuous-wave ENDOR for very sharp resonances Pulsed ENDOR with: Selective pulses (Davies) Non-selective pulses (Mims)